Year: 2002
Author: Liu Tang, Shu-Hua Zhang, J. R. Cannon, Yan-Ping Lin, Ming Rao
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 6 : pp. 627–642
Abstract
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method are derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2002-JCM-8948
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 6 : pp. 627–642
Published online: 2002-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Error estimates finite element Sobolev equation numerical integration.